Haynsworth inertia additivity formula

If H11 is singular, we can still define the generalized Schur complement, using the Moore–Penrose inverse H_{11}^+ instead of H_{11}^{-1}. The formula does not hold if H11 is singular. However, a generalization has been proven in 1974 by Carlson, Haynsworth and Markham, to the effect that \pi(H) \ge \pi(H_{11}) + \pi(H/H_{11}) and \nu(H) \ge \nu(H_{11}) + \nu(H/H_{11}) . Carlson, Haynsworth and Markham also gave sufficient and necessary conditions for equality to hold. == See also ==